document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61442>Question 61442</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534419860/algebrahomeworkh>Calculus for the Managerial, Life, and Social Sciences</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular box is to have a square base and a volume of 20 feet cubed.  If the material for the base costs $.30/square foot, the material for the sides costs $.10/square foot, and the material for the top costs $.20/square foot, determine the dimensions of the box that can be constructed at minimun cost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42315 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=42315\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = side of square base in feet<BR>\n" );
document.write( "h = height of box in feet<BR>\n" );
document.write( "cost of base = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.30x%5E2 ALIGN=MIDDLE  ALT=\".30x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cost of 4 sides = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.10%2A4%2Ah%2Ax ALIGN=MIDDLE  ALT=\".10%2A4%2Ah%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cost of tgop = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.20x%5E2 ALIGN=MIDDLE  ALT=\".20x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.3x%5E2+%2B+.4xh+%2B+.2x%5E2 ALIGN=MIDDLE  ALT=\"C+=+.3x%5E2+%2B+.4xh+%2B+.2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29h+=+20 ALIGN=MIDDLE  ALT=\"%28x%5E2%29h+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > volume of box = 20 ft3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+20%2Fx%5E2 ALIGN=MIDDLE  ALT=\"h+=+20%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.3x%5E2+%2B+.4x%2A%2820%2Fx%5E2%29+%2B+.2x%5E2 ALIGN=MIDDLE  ALT=\"C+=+.3x%5E2+%2B+.4x%2A%2820%2Fx%5E2%29+%2B+.2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.3x%5E2+%2B+8%2Fx+%2B+.2x%5E2 ALIGN=MIDDLE  ALT=\"C+=+.3x%5E2+%2B+8%2Fx+%2B+.2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+.5x%5E2+%2B+8%2Fx ALIGN=MIDDLE  ALT=\"C+=+.5x%5E2+%2B+8%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I make a table<BR>\n" );
document.write( "x = 1<BR>\n" );
document.write( "C = 8.5<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "C = 6<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "C = 7.17<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "C = 10<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "It looks like x = 2 may give a minimum cost<BR>\n" );
document.write( "I tried x = 1.8 and x = 2.2<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "x = 1.8<BR>\n" );
document.write( "C = 6.06<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "x = 2.2<BR>\n" );
document.write( "C = 6.06<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "so, C=6 really is a min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2h+=+20 ALIGN=MIDDLE  ALT=\"x%5E2h+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h+=+20 ALIGN=MIDDLE  ALT=\"4h+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+5 ALIGN=MIDDLE  ALT=\"h+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2x2x5 are the dimensions for min cost = $6.00 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );